Chapter 16
Predator-Prey Coevolution
Linda R. Van Thiel
Department of Biological Sciences
Wayne State University
Detroit, Michigan 48202
(313) 577-2776
Linda is the laboratory coordinator for the introductory biology course for nonmajors and the two-semester freshman biology sequence for majors at Wayne
State University. Linda received her B.S. in Biology from Northern Illinois
University in 1973 and her M.S. in Physiology from Michigan State University in
1977. She has been in her present position since 1977. In addition to writing
organizational materials and selected handouts for the three courses she
coordinates, Linda has written a laboratory manual entitled Laboratory Exercises
in Biology: From Chemistry to Sex, now in its third edition. She has also prepared
pedagogical materials for the biology text authored by Peter Raven and George
Johnson, published by Mosby Year Book; these materials include the extensive
Instructor’s Resource Manual that accompanies the text. Her research interests
include introductory laboratory instruction and the development of fool-proof,
inexpensive laboratory exercises.
Reprinted from: Van Thiel, L. R. 1994. Predator-prey coevolution. Pages 293-318, in Tested studies for
laboratory teaching, Volume 15 (C. A. Goldman, Editor). Proceedings of the 15th Workshop/Conference of the
Association for Biology Laboratory Education (ABLE), 390 pages.
- Copyright policy: http://www.zoo.utoronto.ca/able/volumes/copyright.htm
Although the laboratory exercises in ABLE proceedings volumes have been tested and due consideration has been
given to safety, individuals performing these exercises must assume all responsibility for risk. The Association for
Biology Laboratory Education (ABLE) disclaims any liability with regards to safety in connection with the use of
the exercises in its proceedings volumes.
© 1994 Linda R. Van Thiel
293
Association for Biology Laboratory Education (ABLE) ~ http://www.zoo.utoronto.ca/able
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Predator-Prey Coevolution
Contents
Introduction....................................................................................................................294
Materials ........................................................................................................................295
Notes for the Instructor ..................................................................................................296
Additional Directions.....................................................................................................296
Computer Instructions....................................................................................................296
Variations on the Theme................................................................................................297
Student Outline ..............................................................................................................298
Introduction....................................................................................................................298
Procedures......................................................................................................................301
Predator Calculations.....................................................................................................303
Prey Calculations ...........................................................................................................304
Student Questions ..........................................................................................................305
Appendix A: Tables for Data Collection .......................................................................306
Appendix B: Further Reading........................................................................................307
Appendix C: Predator-Prey Worksheet Formulae .........................................................308
Appendix D: Predator-Prey New Predator Number Formulae ......................................309
Appendix E: Macintosh Excel Spreadsheet Tables .......................................................310
Appendix F: Sample Data Tables and Graphs...............................................................310
Introduction
This laboratory exercise is distinctly different from the multitude of exercises that examine the
fluctuations of prey and predator populations over many generations, that is, the typical rabbit-fox
or deer-wolf situations. This exercise mandates that the total populations of prey and predator do
not change over time. What may change is the number of individuals of each phenotype morph for
prey and predators through interactive selective forces. If each predator morph captures
approximately the same number of each prey morph, the numbers of each predator and prey morph
in successive generations will not change significantly. When one predator morph captures
significantly more or fewer prey, the numbers of each of the predator morphs change in the next
generation. Similarly, if one prey morph is captured to a greater or lesser extent than the others, the
number of each prey morph will change in the next generation. In this respect, therefore, this
exercise does truly examine the evolution of a species and co-evolution of two interacting species as
the numbers of each predator and prey morph change over successive generations. In addition to
examining the selective pressures incurred by the type of predator morph, performing this exercise
as described using two habitats examines the additional selective pressures conferred by the habitat.
This provides for further discussions relating ecology and evolution.
We have successfully presented this laboratory exercise at three different levels: introductory
non-majors, introductory majors, and sophomore/junior ecology. The students at the introductory
levels are not expected to understand the predator-prey calculations as fully as the ecology students.
The amount of time spent on the theoretical background and the predator and prey calculations
therefore needs to be adjusted accordingly. The beginning students are also provided with
computer-generated data tables and graphs. The more advanced students are expected to construct
their own tables and graphs.
The optimum number of students foraging at any one time is probably 12, initially 4 of each
predator, although we have worked with groups as small as 6 and as large as 15. The size and shape
of the habitat area (i.e., lab table) further dictate the optimal number. If the class size is large
enough, both habitats should be run simultaneously otherwise there may not be enough time in a 3-
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hour lab to introduce the topic, perform the exercise, and discuss the results. The procedures in the
Student Outline, though, are written so that the two habitats are run sequentially. In all three
classes, we expect the students to write a laboratory report. Again, the prepared tables and graphs
ensure that all of the students in the less advanced classes start at the same point. The first time the
exercise was performed with the introductory non-majors they were expected to construct their own
graphs. Unfortunately, very few of the students had the ability to do this well. Their analysis of the
data, therefore, suffered. At this level, I feel that the analysis of the data is the more important
concept and thus I constructed a computer spreadsheet to generate the graphs. This spreadsheet also
ensures accuracy, substantially reduces the time spent calculating the next generation values, and
allows more time for discussing the results.
In general, this is an entertaining, easily performed, inexpensive laboratory exercise. Dried
beans are most readily obtained at a bulk foods store. Other types of prey can be substituted as well
as indicated in the section entitled Variations on the Theme. I strongly recommend that plastic
utensils be used the first time around just in case the first time is also the last time. If deemed
successful, sturdy silverware is obtained more cheaply at a restaurant supply or warehouse store.
When nature and class size allow, this exercise is best performed outside using a section of wide
sidewalk and an equally-sized expanse of lawn as the two habitats. One drawback though, is that it
is virtually impossible to collect all of the prey at the end of the exercise and one can expect to
provide a full complement of prey for each laboratory section.
Several problems are possible with this laboratory exercise. For some reason, the students want
to return the prey captured in a round and add back the calculated number as well. This is not
appropriate! To prevent this, make sure that they give you (the “Supreme Ruler”) their prey
immediately after counting them. Collect each morph and then have the students count the number
to be added for the next generation from this pool. Occasionally, the person entering data does it
improperly by paying poor attention to the predator/row or prey/column distinctions. This often
goes unnoticed. Although the evolutionary trends are affected, the exercise is not ruined unless
numbers of prey captured are entered in a row in which a predator morph has become extinct. If
this occurs on my spreadsheet, the total for that row (the extreme right hand column) will return the
phrase “no forks!” (or knives, or spoons) as a warning. Similarly if more prey are reported captured
than were initially in the environment, the total for that morph column will report the phrase “too
many!” If more prey of all morphs are reported captured than were known to be in the environment,
the total number of prey cell will report the phrase “OOPS!”
Materials
This list assumes a class of 24 students with both habitats running concurrently:
Student collection cups (24)
Silverware morph: fork, knife, spoon (24 of each)
Dried bean morphs: garbanzo, lentil, lima, pea (2 packages of exactly 500 for each)
Extra dried bean morphs: garbanzo, lentil, lima, pea (2 packages of about 500 for each)
Prey stockade cups (labeled): garbanzo, lentil, lima, pea (8)
Foam mattress pad
Calculators (minimum of 2)
Computer with printer (optional, but strongly recommended)
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Notes for the Instructor
Additional Directions
When there are multiple sections of a course being run, the first instructor should use the prey in
the counted packets of 500 to start the exercise. Use the prey in the uncounted packets to add to the
prey morphs that are increasing in the second and third generations. Leave the excess prey for the
morphs that are decreasing in the appropriate prey stockade. Use the uncounted prey to replace prey
that become physically damaged or those that escape where you cannot reach them (i.e., down a
drain, under a cabinet).
At the end of each class you must return the total number of each prey to 500. This should be
fairly easy to do since you have the total count for each predator for the last round. Add or subtract
to make 500 and place these in the appropriate package for 500. Any prey over 500 should be put in
the appropriate uncounted packet(s). If for any reason you cannot return the total to 500, leave a
note so that the next instructor does not start his/her session blindly with incorrect numbers!
With regard to predators, if your class is not evenly divisible by three you may elect to
participate as a predator if you are short by only one. Alternately, you may select one or two
students whose counts will be doubled. Produce graphs for each generation via the computer if one
is available. Reduce, then cut and paste (or tape) two or three graphs per page, and finally
photocopy for each student in your class.
Computer Instructions
All of the calculations necessary to do this experiment have been entered on a computer
spreadsheet available from the author. Both Macintosh and MS-DOS versions are available. The
Mac version is written in Excel 4.0. This spreadsheet can also be directly imported into MS-DOS
Excel for Windows. The MS-DOS versions available include the earliest version of Lotus 1-2-3
(extension *.wks), version 2 of the same program (extension *.wk1), an early version of Borland’s
Quattro (extension *.wkq), and a later version of Borland’s Quattro Pro (extension *.wq!). In
general, the near-universal spreadsheet standard is the Lotus 1-2-3 *.wks file. I have found that
nearly every spreadsheet, database, or word processing program can import such a file with very
little difficulty. Consult the reference manual for the program available to you. The only negative
point associated with importing the basic *.wks file is that it is so primitive that the warning phrases
described in the fifth paragraph of the Introduction cannot be implemented.
I will be glad to send a copy of the spreadsheet file(s) to any one requesting them. Please send a
formatted disk or a check for $3.00 US to me and indicate what type of computer system(s) and
spreadsheet program(s) you have available. As we have used both Quattro Pro and Macintosh Excel
4.0, I have basic directions for those programs available as well and will send you whichever seems
most appropriate. You may need to restructure some of the graphic and printing parameters
associated with the spreadsheet files to accommodate your specific computer system and printer.
To prevent the inadvertent over-writing of any formulae in the spreadsheet, data can be entered
only in the specified area, the brighter or different-colored portion of the screen. The rest of the
spreadsheet is protected without a password. The data and calculations for each generation are
visible on a single computer screen and are analogous to the tables present in the student's exercise.
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Variations on the Theme
Substitute other silverware morphs for the common fork, knife, and spoon. These could include
the morphs of the large species Argentum megaserverous, specifically the meat fork, serving spoon,
and carving knife. Obtaining these morphs, though, is significantly more costly for the Supreme
Ruler. One could also enlist the species at the opposite end of the spectrum, Argentum humiliorus,
that include the seafood fork, butter knife, and sugar spoon. Interesting data could also be acquired
through the use of hybrid morphs like the grapefruit spoon with its serrated projections on its
anterior edge.
Substitute mutant plasticware for silverware. These forms are nearly identical in physical and
behavioral attributes but lack the hard, shiny exoskeleton of the typical Argentum species. They are,
therefore, quite brittle and have a much lower survival rate over time than the non-mutants. For this
reason each plasticware individual produces significantly greater numbers of progeny in each
successive generation than do the typical morphs that reproduce only to replace their own numbers.
Plasticware probably most closely follows a Type III survivorship curve, while silverware more
closely follows a Type I or Type II curve. The mutant hybrid spork, commonly found in fast food
restaurants, would be an especially curious morph to test. It is a mutant with the additional hybrid
attributes of the grapefruit spoon.
Substitute other prey for the dried beans. One could use the multi-morphed prey, Pasta
nonebullientum, that originated in China, but established significantly greater morphological
diversity on the Italian peninsula. Cerealis frigidus is a type of prey enjoyed by silverware
predators due to their ability to store sugar in very high amounts. This species is amphibious and
inhabits both terrestrial and aquatic habitats. While most dry cereal morphs behave similarly on
land, when immersed in liquid some remain crunchy and others become soggy, some float and
others sink. A most interesting morph, commonly called the rice crispy, elicits a mating call when
aquatic and can be identified by its characteristic “snap, crackle, pop.”
Provide various colored and textured habitats on which the predators and prey can coevolve. A
deep pile shag carpet provides a jungle-like habitat in which the smaller prey can readily hide. The
sharper-toothed predators also have a tendency to get caught in the entwined strands. This can also
be turned into an outdoor laboratory exercise providing such habitats as a sandbox, a small wading
pool, a sidewalk or driveway, and/or a patch of lawn. In the latter example especially, one should
provide substantially greater quantities of prey morphs as it will be impossible to collect the strays
when the exercise is completed. At least though, the lost prey will be used as a food source by other
furry and feathery prey organisms.
Finally, one could assign students to physically adapt their predator to better capture one or
more prey morphs. Alternately, adapt the prey to better evade capture by one or all predators.
Determine whether such adaptation will prescribe to gradualism or punctuated evolutionary trends.
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Student Outline
Introduction
Living organisms within a community interact in a variety of ways. The primary relationship
between predator and prey is a familiar one. The predator organism finds the prey organism and uses it
as a source of nutrition. It is quite obvious that this relationship is beneficial for the predator and
deleterious for the prey. Through the process of evolution, a prey population with sufficient species
diversity can, over time, change with respect to being preyed upon to increase their survivability.
Some of the organisms within the population may display characteristics that decrease their
chance of being eaten. These characteristics confer a reproductive advantage, the individuals survive,
reproduce, and have a greater number of offspring that exhibit these positive characteristics. Other
organisms may display negative characteristics that result in a greater chance of being preyed upon.
Their traits will decrease within the population as these organisms fail to reproduce and pass on their
traits. Through the process of natural selection these individuals are said to be selected against. Those
with positive traits will become more common in future populations. Individuals within a species that
have slightly different visible characteristics, or phenotypes, are called morphs. The genetic variation
present is not significant enough to qualify the individuals as being different species. The existence of
morphs merely reflects the overall genetic diversity within a species.
Many forces within nature act upon the predator population that are not directly related to
predation but nonetheless affect survival and reproductive fitness. Individuals that are well equipped to
escape from predators may succumb to disease while enough of those that are good prey (at least to the
predator) may survive to reproduce and pass on their genes. Because these natural forces change from
year to year, the characteristics of individuals within a population vary over time. Traits that are
reproductively advantageous one year may be deleterious the next. As a result, a great degree of genetic
diversity is maintained within a species over time. This diversity enables a species to survive totally
unexpected changes in the environment. Contrary to popular opinion, an alteration in the environment
does not cause a change in an individual's genes. Rather it affects the entire population by allowing only
those with an already different genetic pattern to survive.
The peppered moth (Biston betularia) provides one of the best known examples of morph success
in varying environments. Prior to the industrial revolution in Britain, the peppered moth existed
primarily in its light-colored morph. These individuals were nearly invisible on the light lichen-covered
trees on which they rested. A dark morph of the peppered moth existed, but individuals were rare as they
were easy targets for birds. Surprisingly, the gene for dark coloration is dominant over the light gene.
As industry increased, the tree trunks became darkened and the lichens were killed by the pollutants. The
light-colored moths became the easy prey against the darker background while the dark individuals
became difficult to spot. As a result fewer of the light morph and more of the dark morph survived to
reproduce. The population of pepper moths in the industrialized areas shifted to the dark variety. In nonpolluted areas though, the light-colored moth remained the predominant morph. The peppered moth, a
prey species, therefore exhibits two morphs each with a greater or lesser ability to escape predation
relative to the environment.
Similarly, predators have morphs with different abilities to capture prey. A complex interaction
exists between predator and prey species, and between each of them and its environment that enables
each to survive, reproduce, and evolve. The evolution of each species is so closely connected with the
evolution of the other that the two are said to coevolve with respect to one another. It is the interactive
selection associated with this process that will be examined in this laboratory exercise. A simple series
of encounters will illustrate how the physical and behavioral traits of different morphs of prey affect the
survival and reproduction of each predator morph and vice versa.
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299
The predator in this exercise is the steely Argentum utensilum, commonly known as silverware
(Figure 16.1). This ferocious species exhibits numerous morphs, the most common of which are the
dinner knife, dinner fork, and teaspoon. Although the business end of each morph appears quite
different, all possess a streamlined body that enables them to streak across the surface of their environs.
All three morphs possess a mirror-like coat that reflects images of the habitat, confuses their prey and
blinds them in bright sunlight. The favorite prey of all silverware is the meek, unassuming dried bean,
Leguminus desicantus. In its mature form, the dried bean is protected by a hard coat that resists the
stabbing of the fork predator morph and the smashing of the knife and spoon morphs. The bean also
exhibits several morphs including the small, round pea; the large, nearly flat lima; the small, ovoid lentil;
and the obese, rotund garbanzo. The peas and garbanzos are the more active of the four morphs and
nimbly roll away from their captors. The dried bean is widespread, but proliferates in two primary
habitats: the hard, flat, homogenous tabletop tundra and the soft, pliable hills and valleys of the foam
mini-mountains.
Every student in the class assumes the identity of a silverware predator and forages for the elusive
dried bean prey. Each series of foraging between predator and prey corresponds to one reproductive
cycle. At the end of each series, the number of each prey and predator morph will be adjusted according
to calculations performed by the laboratory instructor (a.k.a. the Supreme Ruler). The bean morphs that
succeed at evading capture will have their numbers increased as they produce a greater number of
offspring. Those that are readily preyed upon will decrease in number in the next round as an ingested
bean cannot reproduce. The frequency of each bean morph will, therefore, change in subsequent
foraging series. Similarly, the frequency of each predator morph will change according to its success, or
lack thereof. A silverware that captures many beans can produce a greater number of offspring; one that
captures few or none cannot reproduce. The frequency of the successful predator will increase while the
frequency of the poor predator will decrease. A highly unsuccessful predator may, in time, totally
disappear from a given habitat.
The total number of predators and prey remains constant through all generations, only the
frequency of each morph changes. Therefore, the predator and prey populations evolve as the
frequencies of the morphs change. Since the frequency of predator morph is dependent on the prey
morph, the two are coevolving over time. The way in which this coevolution progresses may also be
affected by the habitat in which the foraging takes place. The final analysis of this exercise will include
comments about the coevolution in each habitat as well as a comparison between the two habitats.
The initial assignment of student to predator is random. If a predator morph frequency decreases,
the Supreme Ruler decides which student predator lives or dies. Since the total number of predators
remains constant, the dead predator has the opportunity to be born again as a potentially more successful
predator. As in all natural communities, there are several rules that control the foraging for prey by
predators. These include, but are not limited to, those listed below:
1.
2.
3.
4.
5.
6.
7.
Forage with silverware only — Argentum predators do not have hands!
Bean morphs can be captured only one at a time. Mass preying is not allowed.
Captured beans must be placed in the forager's collecting cup before foraging can continue.
Any bean that escapes the cup must be returned to the habitat.
A predator cannot physically alter its shape.
Predators cannot interfere with other predators.
Predators cannot steal the prey of others as long as the prey is in physical contact with the predator or
his/her collecting cup.
8. The Supreme Ruler will pick up and return any prey that escape the habitat.
The calculations for the predator and prey frequency adjustments are presented after the laboratory
procedures. Students are not required to memorize these equations nor are they expected to perform the
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class calculations. A knowledge of how each equation serves to change numbers and frequencies of
predator and prey morphs will help, though, in determining whether and how coevolution is progressing.
Figure 16.1. Predator and prey morphs.
(Creatively drawn by Dr. Kyle Geran.)
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301
Procedures
1. Randomly scatter 500 dried beans of each prey morph across the tabletop tundra habitat. Pick
up any that fall into the sink canyon or on the floor abyss.
2. The Supreme Ruler will divide the class into three equal groups and randomly assign each
group to be either a knife, fork, or spoon predator morph. He/she will distribute the silverware
appropriately.
3. Enter the numbers of each predator and prey morph on the top and along the left side of the
Tundra First Generation results table (Table 16.1).
4. The Supreme Ruler will signal the onset of the first round of foraging and allow it to continue
for 3 minutes. Predators must follow the foraging rules previously stated!
5. After the first round is completed, each predator will count the number of each prey morph it
captured and calculate the total number of prey. Enter this data in the Tundra First Generation
results table and report it to the Supreme Ruler as well.
6. Place the captured beans in the appropriate prey stockades. Do not return the prey to the
habitat.
7. Data from the entire class will be tabulated by the Supreme Ruler and shared with all students.
He/she will use this data to calculate the numbers of predators and prey for the next round of
foraging. Record the results of the Supreme Ruler's calculations at the bottom of the Tundra
First Generation results table (Table 16.1).
8. Adjust the student predator identities as instructed by the Supreme Ruler. Using prey from the
stockade, add the appropriate number of each bean morph to the habitat as instructed by the
Supreme Ruler. Enter the new numbers of predators and prey at the top and along the left side
of the Tundra Second Generation results table (see Appendix A).
9. Begin the second 3-minute round of tundra foraging. Repeat steps 3 to 8 compiling results for
the second generation.
10. After the Supreme Ruler completes his/her calculations, enter the results in the chart at the
bottom of the Tundra Second Generation results table (see Appendix A).
11. Begin the third 3-minute round of foraging on the tabletop tundra. Repeat steps 3 to 7
compiling results for the third generation. Do not add prey back into the tabletop habitat.
12. After the Supreme Ruler completes his/her calculations, enter the results in the chart at the
bottom of the Tundra Third Generation results table (see Appendix A).
13. Calculate the number of prey in the tabletop tundra habitat. If there are more than 500
individuals of a prey morph, subtract the excess and transfer all individuals of that morph to the
foam mini-mountains habitat. If there are fewer than 500 individuals of a morph, transfer these
to the mountains and add more individuals from the appropriate prey stockade to bring the total
to 500.
14. Students should return to their initial predator identities as determined in step 2. Enter the
numbers of each predator and prey morph on the top and along the left side of the Foam MiniMountains First Generation results table (see Appendix A).
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15. Begin the first 3-minute round of mountain foraging. Repeat steps 3 to 8 compiling results for
the first foam mini-mountains generation.
Table 16.1. Tundra first generation results.
Tabletop Tundra
Prey
1st generation
Garbanzo
Predators
Your
Your
identity
results →
Number of
Morph
individuals
Fork
Number of individuals at start
Lentil
Lima
Pea
Total
Number of individuals caught
Garbanzo
Lentil
Lima
Pea
Total of
all prey
Knife
Spoon
Total of all
predators
Next generation prey
Garbanzo
Add to habitat
New total number
Next generation predator
New numbers
*
* Total number of all prey caught by all predators
Lentil
Lima
Pea
Total
Fork
Knife
Spoon
Total
16. After the Supreme Ruler completes his/her calculations, enter the results in the chart at the
bottom of the Foam Mini-Mountains First Generation results table (see Appendix A).
17. Begin the second 3-minute round of mountain foraging. Repeat steps 3 to 8 compiling results
for the second generation.
18. After the Supreme Ruler completes his/her calculations, enter the results in the chart at the
bottom of the Foam Mini-Mountains Second Generation results table (see Appendix A).
19. Begin the third 3-minute round of foraging on the mountains. Repeat steps 3 to 7 compiling
results for the third generation. Do not add prey back into the foam mini-mountains habitat.
Return all captured prey to the appropriate stockade.
20. After the Supreme Ruler completes his/her calculations, enter the results in the chart at the
bottom of the Foam Mini-Mountains Third Generation results table (see Appendix A).
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303
21. Students should collect all prey and return them to the appropriate morph stockade. Work
collectively to re-establish a package of 500 individuals for each prey morph. Students should
also relinquish their predator and return the silverware to the Supreme Ruler.
22. Study the three data sheets for each habitat and comment on whether and how coevolution
between silverware and dried beans occurred in each habitat. Compare the results between the
tabletop tundra and the foam mini-mountains and comment on the nature of the differences, if
any, in coevolution between the two species.
23. Answer exercise questions and prepare a laboratory report as instructed by the Supreme Ruler.
Predator Calculations
The frequency of a future predator morph is related to the total number of prey captured by all
predator morphs and the number of prey captured by the specific morph. To calculate the number
of morphs of each type of predator for the next round, the following quantities must be known:
1.
2.
3.
4.
5.
The number of predator morphs.
The total number of predators of all morphs.
The frequency of predators of each morph.
The number of prey caught by each predator morph.
The total number of prey caught by all predators.
During the first round there are three predator morphs; this value may decrease as the
population evolves. The total number of predators equals the numbers of students. The frequency
of each predator morph equals the number in that morph divided by the total number of predators.
The total of the frequencies of all morphs cannot be greater than one. In the first round, the
frequency for each morph is 0.33 since each morph represents one-third of the total. This number is
expected to change in subsequent rounds as the population evolves. The final two quantities are
determined during each foraging round.
The new frequency of a predator morph is calculated using the following equation:
(# caught by predator morph ) + old
# caught by all predators
predator morph frequency
For example, if 3 knife morphs caught 50 dried beans, 3 spoon morphs caught 100 beans, and 3 fork
morphs caught 75 beans the number of new knives would be:
225 ⎞
⎛
⎜ 50 ⎟
50 - 75
- 25
3 ⎠
⎝
+ 0.33 =
+ 0.33 =
+ 0.33 = - 0.11 + 0.33 = 0.22
225
225
225
The number of predators in the next round is calculated by multiplying the new morph frequency
by the total number of predators. In the above example, the new number of knives is 0.22 multiplied by
9. The value is 1.98, which rounds off to 2 knives. The average morph is expected to catch 75 dried
beans (= 225/3). Since the knife morph captured only 50 beans, it did less well than expected. As a
result, the number of knife morphs in the next generation is reduced. Similar calculations for the fork
and spoon morphs produces no change in forks (0.33 frequency; three forks) and an increase of one
spoon (0.44 frequency; four total). Note that there is still a total of nine predators and that the
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frequencies add up to approximately one (0.22 + 0.33 + 0.44 = 0.99). It is very important to use the
correct frequency for the calculation of each generation as these numbers are expected change as a result
of each foraging round.
Prey Calculations
To calculate the number of prey the following quantities must be known:
1.
2.
3.
4.
The number of each prey morph that began the round.
The number of all prey that began the round.
The number of each prey morph that was caught in the round.
The total number of all prey caught during the round.
The number of all prey is a sum of the total of each of the prey morphs. Initially, there are 500 of
each prey morph, therefore the number of all prey at the beginning of the first round of foraging equals
2,000. The total number of prey is kept constant at 2,000 through all generations. It is the number of
each prey morph, and thus its frequency, that changes as the population evolves.
The number of prey morphs to be added back to the habitat before the next round of foraging is
readily calculated for each morph. This value may be equal to the numbers of a prey morph removed in
capture. This prey morph is average in evading capture by all predators and simply maintains its
numbers in the population (analogous to zero population growth). The value may be less that the
number captured, indicating that the morph is easy prey, many get captured and fewer are available to
reproduce for the next generation. The number added to the habitat may also be greater than the number
captured, indicating an elusive prey morph that subsequently produces a greater number of its type for
the next generation.
The following equation is used to calculate the number of individuals of a prey morph to be added
to the habitat in preparation for the next round of foraging:
(total # prey morph @ start of round) - (# prey morph caught)
x (total # prey caught)
(total # all prey @ start of round) - (# all prey caught)
For example, if the 225 prey caught by the nine predators included 25 garbanzos, 40 limas, 60 peas,
and 100 lentils the number of garbanzos to be added to the next generation would be:
500 - 25
475
x 225 =
x 225 = 0.27 x 225 = 60.2 _ 60
2000 - 225
1775
Therefore the number of garbanzos in the second generation will be 35 more than in the first
generation (60 - 25 = 35). Similarly, 58 limas, 56 peas, and 51 lentils are added to the habitat. Note
that the number added (60 + 58 + 56 + 51) equals the number caught (225) to maintain the 2,000
total population.
The frequency of a prey morph for the next generation is calculated by the equation below.
Note that the numerator (the part above the line) is the number of the morph that starts the next
generation.
(total # prey morph @ start) - (# prey morph caught) + (# prey morph added)
total # prey @ start of round
The total numbers of each prey morph in the second generation are: 535 garbanzos, 518 limas,
496 peas, and 451 lentils. The frequency of each morph is: 0.27 garbanzos, 0.26 limas, 0.25 peas,
and 0.22 lentils (which add up to 1 as required). Since each morph began the round with a 0.25
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frequency (500/2000), the garbanzo and lima frequencies have increased, the pea frequency has
stayed the same, and the lentil frequency has decreased. With respect to its own survival, the lentil
is a poor prey morph. With respect to the silverware, the lentil is the best prey item as it is captured
much more readily than any of the other dried beans.
Note: The data presented in the above examples are strictly hypothetical. Do not expect similar
trends with the experiment performed in class. Do not assume that class data are wrong if they do
not follow the same trends.
Student Questions
1. How does the physical nature of each habitat (color, texture, etc.) affect the ability of each prey
morph to evade capture by all predators?
2. How does the physical nature of each habitat affect each predator morph's ability to capture all
of the dried bean prey? Explain your own predator morph experience(s) in greater detail.
3. Does each predator morph have a prey morph that it is particularly adept at capturing? Explain
your answer. Include an analysis of the physical nature of the prey and predator morphs.
Support your explanation with numerical data from the laboratory exercise.
4. Does each predator morph have a prey morph that it is particularly poor at capturing? Explain
your answer. Include an analysis of the physical nature of the prey and predator morphs.
Support your explanation with numerical data from the laboratory exercise.
5. Does any prey morph evade capture by a particular predator morph especially well? Explain
your answer. Include an analysis of the physical nature of the prey and predator morphs.
Support your explanation with numerical data from the laboratory exercise.
6. Does any prey morph evade capture by a particular predator morph especially poorly? Explain
your answer. Include an analysis of the physical nature of the prey and predator morphs.
Support your explanation with numerical data from the laboratory exercise.
7. Analyze your laboratory data and explain whether or not coevolution between predator and prey
morphs has occurred over three generations on the tabletop tundra.
8. Analyze your laboratory data and explain whether or not coevolution between predator and prey
morphs has occurred over three generations on the foam mini-mountains.
9. Compare the coevolutionary trends between the tabletop tundra and the foam mini-mountains.
Do the prey and predator morphs behave the same or differently in each of the habitats?
Explain your answer.
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APPENDIX A
Tables for Data Collection
Six tables are provided in the Student Outline for students to enter their results. I label these tables
as T.1, T.2, and T.3 for tundra first generation, second generation, and third generation,
respectively. Similarly, the tables for the Foam Mini-Mountain habitat are labeled M.1, M.2, and
M.3. A table for tundra first generation (Table 16.1) is given in the Student Outline in this chapter.
The remaining five tables are identical in appearance; in the upper-left cell the habitat and
generation are added (see Table 16.1).
Garbanzo
Predators
Your
Your
identity
results →
Number of
Morph
individuals
Fork
Prey
Number of individuals at start
Lentil
Lima
Pea
Total
Number of individuals caught
Garbanzo
Lentil
Lima
Pea
Total of
all prey
Knife
Spoon
Total of all
predators
Next generation prey
Garbanzo
Add to habitat
New total number
Next generation predator
New numbers
*
* Total number of all prey caught by all predators
Lentil
Lima
Pea
Total
Fork
Knife
Spoon
Total
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APPENDIX B
Further Reading
Abrahamson, W. G. 1988. Plant-animal interactions. McGraw-Hill Book Co., New York, 480
pages
Begon, M., L. Harper, and C.R. Townsend. 1990. Ecology. Second edition. Blackwell Scientific
Publications, Boston, Massachusetts, 876 pages.
Cockburn, A. 1991. An introduction to evolutionary ecology. Blackwell Scientific Publications,
Boston, Massachusetts, 370 pages.
Futuyma, D. J. 1986. Evolutionary biology. Sinauer Associates, Sunderland, Massachusetts, 600
pages.
Gilpin, M. E. 1975. Group selection in predator-prey communities. Princeton University Press,
Princeton, New Jersey, 108 pages
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APPENDIX C
Predator-Prey Worksheet Formulae
(Refer to Table 16.2 in Appendix E)
Total All Predators (cell B14): The sum of the number of individual forks, knives, and spoons. These data
are entered into the spreadsheet in the first generation for each habitat and are calculated in subsequent
generations.
Number of Predator Morphs (cell B16): The difference between the sum of the possible morphs (always
three) and the morph categories that are equal to zero (uses a Criterion Table).
Total Number of Each Prey Caught (cells D14, E14, F, or G14): The sum of the number of each prey caught
by all three predator morphs. If this value exceeds the initial number of prey present then a warning “too
many!” appears to alert the instructor.
Total Number of Prey Caught By Each Predator (cells H10 to H12): The sum of the total number of prey
caught by each predator morph. If a there were no individuals of a certain morph and a value greater than
zero is entered is entered in any of the prey cells, a warning appears to alert the instructor. The warning
depends on the predator morph category (i.e., “no forks!”).
Total Number of Prey Caught By All Predators (cell H14): A summation of all prey caught by all predators
in a given round of capture. The sum of cells D14 to G14 equals the sum of cells H10 to H12. A warning of
“OOPS!” appears to the instructor if this value exceeds the number of prey ultimately available (i.e., 2,000).
Number of Each Prey to Add Back to the Habitat (cells D19, E19, F19, and G19): The number of each prey
to be returned to the habitat after a round of capture. It is related to the total number of prey caught, as
explained in depth within the text of the exercise under the heading Prey Calculations. If this value is a
decimal, it is rounded.
Total Number of Prey to Add Back to the Habitat (cell H19): The sum of the calculated values for each of
the prey.
New Total Number of Each Prey in the Next Generation (cells D20, E20, F20, and G20): The sum of the
number of each prey caught plus the number added back to the habitat subtracted from the original number of
each prey morph present.
New Total Number of Prey in the Next Generation (cell H20): The sum of the total number of each prey for
all prey morphs. As a result of rounding the number of prey added calculation (E19 through G19), the total
number of prey may fluctuate between 1,999 and 2,001.
New Numbers of Each Predator (cells E23, F23, and G23): The number of each predator available for the
next round of capture. It is related to the total number of prey caught, and the number caught by each
predator. This calculation is explained in depth within the text of the exercise under the heading Predator
Calculations. If the value is a decimal it is adjusted to be an integer through a series of conditional equations
that are explained in depth in Appendix D. If the Total All Predator values equal zero, each of these values
are entered as zero. This prevents unusual error messages from appearing prior to any data entry.
New Numbers of All Predator (cell H23): The sum of the values for each new predator number, which is
always equal to the original number of predators. If the Total All Predator value equals zero, this value is
also zero, preventing unusual error messages from appearing prior to any data entry.
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APPENDIX D
Predator-Prey New Predator Number Formulae
(Refer to Table 16.3 in Appendix E)
Round (K16, L16, and M16): Rounds the calculated New Predator Number (NPN) higher or lower.
[Similar syntax in Lotus 1-2-3, Quattro and Excel.]
Integer (K17, L17, and M17): Truncates the calculated NPN by deleting all numbers to right of the
decimal. [Lotus 1-2-3 and Quattro use INTEGER syntax, Excel uses TRUNC syntax.]
# - Round (K18, L18, and M18): Subtracts the rounded NPN from the calculated NPN, resulting in
a positive or negative decimal value. [Similar syntax in Lotus 1-2-3, Quattro and Excel.]
# - Integer (K19, L19, and M19): Subtracts the truncated NPN from the calculated NPN, resulting
in a positive or negative decimal value. [Similar syntax in Lotus 1-2-3, Quattro and Excel.]
1st Conditional (K20, L20, and M20): If the Total All Predators value (sum of values in the leftmost column) and the sum of the Round NPN values are equal, the number entered here is the NPN
Round value. If they are not equal, but NPN Round equals NPN Integer, the number entered here is
again the NPN Round value. If neither of the previous conditions are true and the NPN # - Round
decimal value is less than the NPN # -Integer decimal value, then the number entered here is the
NPN Integer value. Generally, NPN Round is the chosen value, unless this choice causes an
increase in the total number of predators. [Nested IF statements with similar syntax in Lotus 1-2-3,
Quattro and Excel.]
2nd Conditional (K21, L21, and M21): If the Total All Predators value and the sum of the Round
NPN values are equal, the number entered here is the NPN Round value. If they are not equal, but
NPN Round equals NPN Integer, the number entered here is again the NPN Round value. If neither
of the previous conditions are true and the individual NPN # - Integer value is the maximum # Integer value for all predators then the number entered here is the NPN Integer value. Generally,
NPN Round is the chosen value, unless this choice causes an increase in the total number of
predators. [Nested IF statements with similar syntax in Lotus 1-2-3, Quattro and Excel, the former
use “..” to separate the extremes in the MAX function, Excel uses a colon.]
3rd Conditional (K22, L22, and M22): On rare occasions with certain data, the total number of
predators becomes smaller than the initial number. As this is not allowed by the Rules, this
statement compares the 1st and 2nd Conditional values. The larger of the two values is entered
here. [Simple IF statement with similar syntax in Lotus 1-2-3, Quattro and Excel.]
4th Conditional and the Next Value (K23, L23, and M23): On rare occasions with certain data, the
total number of predators becomes larger or smaller than the initial number. As this is not allowed
by the Rules, when the sum of the 3rd Conditional values is greater then the initial Total All
Predators value the difference between these two values is subtracted from the predator morph with
the greatest number of individuals. [IF statement combined with an AND and an OR function.
Lotus 1-2-3 and Quattro use a straightforward “1ST CONDITION AND 2ND CONDITION,
TRUE” syntax; Excel syntax is “AND(1ST CONDITION, 2ND CONDITION,TRUE)”.]
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APPENDIX E
Macintosh Excel Spreadsheet Tables
Tables 16.2 and 16.3 (pages 311 and 312) show the formulae associated with the worksheet
calculations described in Appendix C and those associated with the new predator number
conditionals described in Appendix D.
APPENDIX F
Sample Data Tables and Graphs
The tables and graphs on pages 313–318 contain data derived at the morning session of my
Predator-Prey Coevolution Workshop at the 1993 ABLE Conference in Toronto, Canada. The
computer system was used a Macintosh IIsi with a Personal Laserwriter printer. The software used
was Microsoft Excel 4.0.
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